A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and radius 'R' (< L) is attached at its centre to the free end of the rod. Consider two ways the disc is attached: (case A) - The disc is not free to rotate about its centre and (case B) - the disc is free to rotate about its centre. The rod-disc system after being released from the same displaced position. Which of the following statement(s) is(are) true?

Options

A. Restoring torque in case `A` = Restoring torque in case`B`
B. Restoring torque in case `A lt` Restoring torque in case`B`
C. Restoring frequency case `A gt` Angular frequency for case`B`
D. Restoring frequency case `A lt` Angular frequency for case`B`

Answer

A, D

Explanation

Tprque is same for both the cases.
`T = 2pisqrt((I)/(mgd))`
`I_(A) gt T_(B)`
`omega_(A) lt omega_(B)`